1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}, \lambda \vec{b}+4 \vec{c}$ and $(2 \lambda-1) \vec{c}$ are non-coplanar for

A
no value of $\lambda$.
B
all except one value of $\lambda$.
C
all except two values of $\lambda$.
D
all values of $\lambda$.
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{a} \times \vec{b}|^2=k^2-(\vec{a} \cdot \vec{b})^2$, then the values of $k$ and $\theta$ are

A
$k=1, \theta=45^{\circ}$
B
$k=7, \theta=60^{\circ}$
C
$k=49, \theta=90^{\circ}$
D
$k=7$ and $\theta$ is arbitrary
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ is $\alpha, \vec{b}$ and $\vec{c}$ is $\beta$ and $\vec{c}$ and $\vec{a}$ is $\gamma$. Then the minimum value of $\cos \alpha+\cos \beta+\cos \gamma$ is

A
$\frac{1}{2}$
B
$-\frac{1}{2}$
C
$\frac{3}{2}$
D
$-\frac{3}{2}$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the parallelogram for which $\vec{\alpha}$ and $\vec{\beta}$ are adjacent sides is

A
$\sqrt{17}$
B
$\sqrt{14}$
C
$\sqrt{7}$
D
$\sqrt{41}$
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